Applying Boolean Breaks Topology
Judging from the rounded surfaces and the post-application deformations, I'd wager that you have an unapplied Subdivision Surface modifier. Once you've applied the boolean operation without applying the subsurf, the subsurf operation is now operating on the circular cutouts as well as the original mesh.

Consider not applying the boolean operation if possible. One of the biggest advantages of the boolean workflow is the procedural aspect of it. If not, backup the model and apply all other modifiers before applying the boolean.